Jessica hikes east for 9 miles, then turns and hikes south for 12 miles. What is the distance, in miles, of the shortest route back to her starting location?
Solution: Her path forms a right triangle, since east and south are perpendicular to each other. The shortest route back is the hypotenuse of this right triangle, which equals $\boxed{15}\text{ miles}$ (a multiple of a 3-4-5 right triangle). [asy] draw((0,0)--(9,0)--(9,-12)); draw((0,0)--(9,-12),dashed); draw(rightanglemark((0,0),(9,0),(9,-12),20)); label("9",(0,0)--(9,0)); label("12",(9,0)--(9,-12)); label("15",(0,0)--(9,-12)); [/asy]